looks like it's stained (which makes sense since the underside shows more grain than the top) and has a layer of something shiny on top of that. It shows along the bottom edge of the sides.

Thanks, Bobert. If the brazil nut or ashes don't do the trick, I'll think about trying a linseed concoction. Will I stick with the grain on that, or do little circles?
If I have absolutely no luck pulling the white out enough to keep it from catching my eye so much, I'll just go with the Tablecloth Routine. I don't want to sand/refinish it..at least not anytime soon.

Do we have anything like Brasso Wadding in the US?